Continuous and Discontinuous Piecewise Linear Solutions of the Linearly Forced Inviscid Burgers Equation

DOI

10.2991/jnmp.2008.15.s3.26How to use a DOI?

Abstract

We study a class of piecewise linear solutions to the inviscid Burgers equation driven by a linear forcing term. Inspired by the analogy with peakons, we think of these solutions as being made up of solitons situated at the breakpoints. We derive and solve ODEs governing the soliton dynamics, first for continuous solutions, and then for more general shock wave solutions with discontinuities. We show that triple collisions of solitons cannot take place for continuous solutions, but give an example of a triple collision in the presence of a shock.

Copyright

© 2008, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - JOUR
AU  - Hans Lundmark
AU  - Jacek Szmigielski
PY  - 2008
DA  - 2008/10/01
TI  - Continuous and Discontinuous Piecewise Linear Solutions of the Linearly Forced Inviscid Burgers Equation
JO  - Journal of Nonlinear Mathematical Physics
SP  - 264
EP  - 276
VL  - 15
IS  - supplement 3
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.2008.15.s3.26
DO  - 10.2991/jnmp.2008.15.s3.26
ID  - Lundmark2008
ER  -